Weak compactness and convergences in LE1[E].- Abstract convexity and non-smooth analysis.- Recursive method in stochastic optimization under compound criteria.- On law invariant coherent risk measures.- The MongeKantorovich problems and stochastic preference relations.It is planned to publish this series once a year under the auspices of the Reserch Center of Mathematical Economics (Tokyo) It is designed to bring together those mathematicians who are seriously interested in obtaining new challenging stimuli from economic theories and those economists who are seeking effective mathematical tools for their research Authors are asked to develop their original results as fully as possible and also to give a clear-cut expository overview of the problem under discussion. Consequently, this series will also invite articles which might be considered too long for publication in journalsSpringer Book Archives